We have to remember that the 30° number is the "Main Axis" of the thin slice beam...or the strongest part of the sound pulse...(just like standing in front of a speaker...the sound is louder directly in front of the speaker and weaker at any angle away from the speaker)...
The sound not only radiates along the "Main Axis"...it also radiates laterally away from the "Main Axis" at the same time...
While your calculation is probably correct that the "Main Axis" will run aground at 21ft away from the xducer in 10ft of water...:
There are still weaker parts of the sound wave are that hitting the ground closer than 21ft (under the 30° "Main Axis" angle...and farther than 21ft (above the 30° "Main Axis" angle)...
The processor and the algorithms designed in the unit determine which echoes in the weaker parts of the sound wave are worthy of being "painted" into the image....and whether those weaker echoes should be painted as fish, structure, or bottom detail...
Rickie


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